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# Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012)

### Overview

Course Features
• Video lectures
• Captions/transcript
• Projects (no examples)
• Assignments: problem sets with solutions
Educator Features
• Instructor insights
Course Description

This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course.

Acknowledgments

Thanks to videographers Martin Demaine and Jayson Lynch.

### Syllabus

Lecture 1: Overview.
Class 1: Overview.
Lecture 2: Simple Folds.
Class 2: Universality & Simple Folds.
Lecture 3: Single-Vertex Crease Patterns.
Class 3: Single-Vertex Crease Patterns.
Lecture 4: Efficient Origami Design.
Class 4: Efficient Origami Design.
Lecture 5: Artistic Origami Design.
Class 5: Tessellations & Modulars.
Lecture 6: Architectural Origami.
Class 6: Architectural Origami.
Lecture 7: Origami is Hard.
Class 7: Origami is Hard.
Lecture 8: Fold & One Cut.
Class 8: Fold & One Cut.
Lecture 9: Pleat Folding.
Class 9: Pleat Folding.
Lecture 10: Kempe's Universality Theorem.
Class 10: Kempe's Universality Theorem.
Lecture 11: Rigidity Theory.
Class 11: Generic Rigidity.
Lecture 12: Tensegrities & Carpenter's Rules.
Class 12: Tensegrities.
Lecture 14: Hinged Dissections.
Class 14: Hinged Dissections.
Lecture 15: General & Edge Unfolding.
Class 15: General & Edge Unfolding.
Lecture 16: Vertex & Orthogonal Unfolding.
Class 16: Vertex & Orthogonal Unfolding.
Lecture 17: Alexandrov's Theorem.
Class 17: D-Forms.
Lecture 18: Gluing Algorithms.
Lecture 19: Refolding & Smooth Folding.
Class 19: Refolding & Kinetic Sculpture.
Lecture 20: Protein Chains.
Lecture 21: HP Model & Interlocked Chains.

### Taught by

Prof. Erik Demaine

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